Use lattice on part of object
The problem can stem from applying scale to the lattice. You shouldn't do it. Apply scale to a chair, create new lattice for the leg and don't apply scale to it. Then this setup should work perfectly, but I would suggest to subdivide the leg little more to get the effect, you need. 
Also in my opinion it would be easier to just use proportional editing directly on the leg vertices to get desired curvature. Lattice doesn't give more control in this particular example.
I would also suggest you to split the chair on 2 and use mirror modifier to ensure, that bending will be exactly the same for both legs.